A Necessary Condition for Byzantine $k$-Set Agreement

This short paper presents a necessary condition for Byzantine k-set agreement in (synchronous or asynchronous) message-passing systems and asynchronous shared memory systems where the processes communicate through atomic single-writer multi-reader registers. It gives a proof, which is particularly simple, that k-set agreement cannot be solved t-resiliently in an n-process system when n ≤ 2t + t k . This bound is tight for the case k = 1 (Byzantine consensus) in synchronous message-passing systems.